The chiral p-wave superconductor/superfluid in two dimensions (2D) is the simplest and most robust system for topological quantum computation [1,2] . Candidates for such topological superconductors/superfluids in nature are very rare. A widely believed chiral p-wave superfluid is the Moore-Read state in the ν = 5 2 fractional quantum Hall effect [3,4], although experimental evidence are not yet conclusive [5]. Experimental realizations of chiral p-wave superconductors using quantum anomalous Hall insulator-superconductor hybrid structures have been controversial [7,8]. Here we report a new mechanism for realizing 2D chiral p-wave superconductors on the surface of 3D s-wave superconductors that have a topological band structure and support superconducting topological surface states (SC-TSS), such as the iron-based superconductor Fe(Te,Se) [9]. We find that tunneling and pairing between the SC-TSS on the top and bottom surfaces in a thin film or between two opposing surfaces of two such superconductors can produce an emergent 2D time-reversal symmetry breaking chiral topological superconductor. The topologically protected anyonic vortices with Majorana zero modes as well as the chiral Majorana fermion edge modes (χMEMs) can be used as a platform for more advantageous non-abelian braiding operations. We propose a novel device for the CNOT gate with six χMEMs, which paves the way for fault-tolerant universal quantum computing.
Majorana-based quantum gates are not complete for performing universal topological quantum computation while Fibonacci-based gates are difficult to be realized electronically and hardly coincide with the conventional quantum circuit models. In reference Hu and Kane (2018 Phys. Rev. Lett. 120 066801), it has been shown that a strongly correlated Majorana edge mode in a chiral topological superconductor can be decomposed into a Fibonacci anyon τ and a thermal operator anyon ɛ in the tricritical Ising model. The deconfinement of τ and ɛ via the interaction between the fermion modes yields the anyon collisions and gives the braiding of either τ or ɛ. With these braidings, the complete members of a set of universal gates, the Pauli gates, the Hadamard gate and extra phase gates for one-qubit as well as controlled-NOT (CNOT) gate for two-qubits, are topologically assembled. Encoding quantum information and reading out the computation results can be carried out through electric signals. With the sparse-dense mixed encodings, we set up the quantum circuit where the CNOT gate turns out to be a probabilistic gate and design the corresponding devices with thin films of the chiral topological superconductor. As an example of the universal topological quantum computing, we show the application to Shor’s integer factorization algorithm.
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